A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is $16.65. Find the number of each coin.

N - nickel

d-dimes

first it is said that we have n+d=9,45

and if we double the dimes we will have

n+2d=16,65

so from the first equation we have n=9,45-d

the second equation then transforms into

n+2d=16,65

9,45-d + 2d=16,65

9,45+d=16,65

d = 16,65-9,45

d=7,2

And we get back to the first equation

n+d=9,45

So n=9,45-d

n=9,45-7,2

n=2,25